Marketing Math: Sample Problems

Horatio Alger has just become product manager for Brand X$.$

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Brand X is a consumer product with a retail price of $$1.$ Retail margins on the product are $33$ percent, while wholesalers take a $12$ percent margin. Brand X and its direct competitors sell a total of $20$ million units annually; Brand X has $24$ percent of this market. Variable manufacturing costs for Brand X are $$\mathrm{.}09$ per unit. Fixed manufacturing costs are $$900,000.$ The advertising budget for Brand X is $$500,000.$ The Brand X product manager$$s salary and expenses total $$35,000.$ Salespeople are paid entirely by a $10$ percent commission.

Shipping costs, breakage, insurance, and so forth are $$\mathrm{.}02$ per unit.

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Using the information above, calculate the following metrics for Brand X $($I recommend using the Marketing Math Sample Problems Template$)$:

$1.$ What is the unit contribution for Brand X$?$

$2.$ What is Brand X$$s break$-$even point?

$3.$ What market share does Brand X need to break even?

$4.$ What is Brand X$$s profit impact?

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Industry demand is expected to increase to $23$ million units next year. Mr$.$ Alger is considering raising his advertising budget to $$1$ million.

$5.$ If the advertising budget is raised, how many units will Brand X have to sell to break even?

$6.$ How many units will Brand X have to sell in order for it to achieve the same profit impact that it did this year?

$7.$ What will Brand X$$s market share have to be next year for its profit impact to be the same as this year?

$8.$ What will Brand X$$s market share have to be for it to have a $$1$ million profit impact?

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Upon reflection, Mr$.$ Alger decides not to increase Brand X$$s advertising budget. Instead, he thinks he might give retailers an incentive to promote Brand X by raising their margins from $33$ percent to $40$ percent. The margin increase would be accomplished by lowering the price of the product to retailers.$$ Wholesaler margins would remain at $12$ percent.

$9.$ If retailer margins are raised to $40$ percent next year, how many units will Brand X have to sell to break even?

$10.$ How many units will Brand X have to sell to achieve the same profit impact next year as it did this year?

$11.$ What would Brand X$$s market share have to be for its profit impact to remain at this year$$s level?

$12.$ What would Brand X$$s market share have to be for it to generate a profit impact of $$350,000?$